I have 40 observations and 32 items and I got non positive definite warning message on SPSS when I try to run factor analysis. Should I increase sample size or decrease items? Or both of them?Thanks
The error indicates that your correlation matrix is nonpositive definite (NPD), i.e., that some of the eigenvalues of your correlation matrix are not positive numbers. If you request a factor extraction method other than principal components (PC) or unweighted least squares (ULS), an NPD matrix will cause the procedure to stop without extracting factors. If one or more of the eigenvalues are negative, then PC and ULS extraction will also terminate.
Matrices can be NPD as a result of various other properties. A correlation matrix will be NPD if there are linear dependencies among the variables, as reflected by one or more eigenvalues of 0. For example, if variable X12 can be reproduced by a weighted sum of variables X5, X7, and X10, then there is a linear dependency among those variables and the correlation matrix that includes them will be NPD. If there are more variables in the analysis than there are cases, then the correlation matrix will have linear dependencies and be NPD. Remember that FACTOR uses listwise deletion of cases with missing data by default. If you had more cases in the file than variables in the analysis, listwise deletion could leave you with more variables than retained cases. Pairwise deletion of missing data can also lead to NPD matrices. Negative eigenvalues may be present in these situations. See the following chapter for a helpful discussion and illustration of how this can happen.
Ref: http://www-01.ibm.com/support/docview.wss?uid=swg21477275
Not necessarily but there is some sort of problem with your data. Try to find someone in Statistics or Mathematics at your University that can help you or provide more information on your data.
Best, David Booth
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